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Scale-free connectivity, small-world pattern, hierarchical modularity and disassortative mixing are prominent features shared by most biological networks. Up to now, various network growth models invoking gene duplication and divergence have been proposed to understand the evolutionary mechanisms shaping the scale-free connectivity, small-world pattern and disassortative mixing . In this paper, we present an evolutionary model by introducing a rule of small preference duplication of a node and sequently divergence plus non-uniform heterodimerization meaning that the probability that an heterodimerization link is added between duplicated nodes is proportional to the number of common neighbors shared by these nodes based on biological background, showing that our model can almost display series of topological characteristics of real protein interaction networks, such as scale-free connectivity, small-world pattern, disassortativity of degree-degree correlation and hierarchical modularity. Our model may yield relevant insights into the evolutionary mechanism of protein interaction networks behind it.
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Keywords:
- protein interaction networks /
- small-preference duplication /
- non-uniform heterodimerization /
- hierarchical modularity
[1] Uetz P, Giot L, Cagney G, Mansfield T A, Judson R S, Knight J R, Lockshon D, Narayan V, Srinvasan M, Pochart P, Emili Q A, Li Y, Godwin B, Conover D, Kalbfleisch T, Vijayadamodar G, Yang M, Johnston M, Fields S, Rothberg J M 2000 Nature 403 623
[2] Ito T, Chiba T, Ozawa R, Yoshida M, Hattori M, Sakaki Y 2001 Proc. Natl. Acad. Sci. USA 98 4569
[3] Guldener U, Munsterkotter M, Oesterheld M, Pagel P, Ruepp A, Mewes H W, Stumpflen V 2006 Nucleic Acids Res. 34 436
[4] Li S, Armstrong C M, Bertin N, Ge H, Milstein S, Boxem M, Vidalain P O, Han J J, Chesneau A, Xu L, Tewari M, Wong S L, Zhang L V, Berriz G F, Jacotot L, Vaglio P, Reboul J, Kishikawa T, Li Q, Gabel H W, Elewa A, Baumgartner B, Rose D J, Yu H, Bosak S, Sequerra R, Fraser A, Mango S, Saxton W M, Strome S, Heuvel S, Piano F, Vandenhaute J, Sardet C, Gerstein M, Stamm L, Cunsalus K, Harper J W, Cusick M E, Roth F P, Hill D E, Vidal M 2004 Science 303 540
[5] Giot L, Bader J S, Brouwer C, Chaudhuri A, Kuang B, Li Y, Hao Y L, Ooi C E, Godwin B, Vitols E, Vijayadamodar G, Pochart P, Machineni H, Welsh M, Kong Y, Zerhusen B, Malcolm R, Varrone Z, Collis A, Minto M, Burgess S, Mcdaniel L, Stimpson E, Spriggs F, Williams J, Neurath K, Loime N, Agee M, Voss E, Furtak K, Renzulli R, Aanensen N, Carrolla S, Bickelhaupt E, Lazovatsky Y, Dasilva A, Zhong J, Stanyon C A, Finley R L, White K P, Braverman M, Jarvie T, Gold S, Leach M, Knight J, Shimkets R A, Mckenna M P, Chant J, Rothberg J M 2003 Science 302 1727
[6] Wanger A 2001 Mol. Biol. Evol. 18 1283
[7] Sole R V, Pastor-Satorras R, Smith E D, Kepler T 2002 Adv. Comp. Syst. 5 43
[8] Jeong H, Mason S P, Barabasi A L, Oltvai Z N 2001 Nature 411 41
[9] Ravasz E, Barabasi A L 2003 Phys. Rev. E 67 026112
[10] Williams R J, Martinez N D, Berlow E L, Dunne J A, Barabasi A L 2002 Science 297 1551
[11] Yook S H, Oltvai Z N, Barabasi A L 2004 Proteomics 4 929
[12] Hase T , Niimura Y, Kaminuma T, Tanaka H 2008 PloS One 3 e1667
[13] Maslov S, Sneppen K 2002 Science 296 910
[14] Vazquez A, Flammini A, Maritan A, Vespignani A 2003 Com- PlexUs 1 38
[15] Chung F, Lu L, Dewey T G, Galas D J 2003 J. Comput. Biol. 10 677
[16] Pastor-Satorras R, Smith E, Sole R V 2003 J. Theor. Biol. 222 199
[17] Ispolatov I, Krapivsky P L, Yuryev A 2005 Phys. Rev. E 71 061911
[18] Ispolatov I, Krapivsky P L, Yuryev A 2005 New J. Phys. 7 145
[19] Dan Z, Liu Z R, Wang J Z 2007 Chin. Phys. Lett. 24 2766
[20] Xu C S, Liu Z R, Wang R Q 2010 Physica A 389 643
[21] Takemoto K, Oosawa C 2005 Phys. Rev. E 71 046116
[22] Takemoto K, Oosawa C 2007 Math. Bios. 208 454
[23] Kellis M, Patterson N, Endrizzi M, Birren B, Lander E S 2003 Nature 423 241
[24] Prachumwat A, Li W H 2006 Mol. Biol. Evol. 23 30
[25] Ohno S 1970 Evolution by Gene Duplication (New York: Springer-Verlag) pp100–110
[26] Evlampiev K, Isambert H 2008 Proc. Natl. Acad. Sci. USA 105 9863
[27] Watts D J, Strogatz S H 1998 Nature 393 440
[28] Zhou Y B, Cai S M, Wang W X, Zhou P L 2009 Physica A 388 999
[29] Newman M E J 2002 Phys. Rev. Lett. 89 208701
[30] Costa L F, Rodrigues F A, Vieso G T, Boas P R V 2007 Adv. Phys. 56 167
[31] Farid N, Christensen K 2006 New J. Phys. 8 212
[32] Li L, Huang Y, Xia X, Sun Z 2006 Mol Biol Evol. 23 12
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[1] Uetz P, Giot L, Cagney G, Mansfield T A, Judson R S, Knight J R, Lockshon D, Narayan V, Srinvasan M, Pochart P, Emili Q A, Li Y, Godwin B, Conover D, Kalbfleisch T, Vijayadamodar G, Yang M, Johnston M, Fields S, Rothberg J M 2000 Nature 403 623
[2] Ito T, Chiba T, Ozawa R, Yoshida M, Hattori M, Sakaki Y 2001 Proc. Natl. Acad. Sci. USA 98 4569
[3] Guldener U, Munsterkotter M, Oesterheld M, Pagel P, Ruepp A, Mewes H W, Stumpflen V 2006 Nucleic Acids Res. 34 436
[4] Li S, Armstrong C M, Bertin N, Ge H, Milstein S, Boxem M, Vidalain P O, Han J J, Chesneau A, Xu L, Tewari M, Wong S L, Zhang L V, Berriz G F, Jacotot L, Vaglio P, Reboul J, Kishikawa T, Li Q, Gabel H W, Elewa A, Baumgartner B, Rose D J, Yu H, Bosak S, Sequerra R, Fraser A, Mango S, Saxton W M, Strome S, Heuvel S, Piano F, Vandenhaute J, Sardet C, Gerstein M, Stamm L, Cunsalus K, Harper J W, Cusick M E, Roth F P, Hill D E, Vidal M 2004 Science 303 540
[5] Giot L, Bader J S, Brouwer C, Chaudhuri A, Kuang B, Li Y, Hao Y L, Ooi C E, Godwin B, Vitols E, Vijayadamodar G, Pochart P, Machineni H, Welsh M, Kong Y, Zerhusen B, Malcolm R, Varrone Z, Collis A, Minto M, Burgess S, Mcdaniel L, Stimpson E, Spriggs F, Williams J, Neurath K, Loime N, Agee M, Voss E, Furtak K, Renzulli R, Aanensen N, Carrolla S, Bickelhaupt E, Lazovatsky Y, Dasilva A, Zhong J, Stanyon C A, Finley R L, White K P, Braverman M, Jarvie T, Gold S, Leach M, Knight J, Shimkets R A, Mckenna M P, Chant J, Rothberg J M 2003 Science 302 1727
[6] Wanger A 2001 Mol. Biol. Evol. 18 1283
[7] Sole R V, Pastor-Satorras R, Smith E D, Kepler T 2002 Adv. Comp. Syst. 5 43
[8] Jeong H, Mason S P, Barabasi A L, Oltvai Z N 2001 Nature 411 41
[9] Ravasz E, Barabasi A L 2003 Phys. Rev. E 67 026112
[10] Williams R J, Martinez N D, Berlow E L, Dunne J A, Barabasi A L 2002 Science 297 1551
[11] Yook S H, Oltvai Z N, Barabasi A L 2004 Proteomics 4 929
[12] Hase T , Niimura Y, Kaminuma T, Tanaka H 2008 PloS One 3 e1667
[13] Maslov S, Sneppen K 2002 Science 296 910
[14] Vazquez A, Flammini A, Maritan A, Vespignani A 2003 Com- PlexUs 1 38
[15] Chung F, Lu L, Dewey T G, Galas D J 2003 J. Comput. Biol. 10 677
[16] Pastor-Satorras R, Smith E, Sole R V 2003 J. Theor. Biol. 222 199
[17] Ispolatov I, Krapivsky P L, Yuryev A 2005 Phys. Rev. E 71 061911
[18] Ispolatov I, Krapivsky P L, Yuryev A 2005 New J. Phys. 7 145
[19] Dan Z, Liu Z R, Wang J Z 2007 Chin. Phys. Lett. 24 2766
[20] Xu C S, Liu Z R, Wang R Q 2010 Physica A 389 643
[21] Takemoto K, Oosawa C 2005 Phys. Rev. E 71 046116
[22] Takemoto K, Oosawa C 2007 Math. Bios. 208 454
[23] Kellis M, Patterson N, Endrizzi M, Birren B, Lander E S 2003 Nature 423 241
[24] Prachumwat A, Li W H 2006 Mol. Biol. Evol. 23 30
[25] Ohno S 1970 Evolution by Gene Duplication (New York: Springer-Verlag) pp100–110
[26] Evlampiev K, Isambert H 2008 Proc. Natl. Acad. Sci. USA 105 9863
[27] Watts D J, Strogatz S H 1998 Nature 393 440
[28] Zhou Y B, Cai S M, Wang W X, Zhou P L 2009 Physica A 388 999
[29] Newman M E J 2002 Phys. Rev. Lett. 89 208701
[30] Costa L F, Rodrigues F A, Vieso G T, Boas P R V 2007 Adv. Phys. 56 167
[31] Farid N, Christensen K 2006 New J. Phys. 8 212
[32] Li L, Huang Y, Xia X, Sun Z 2006 Mol Biol Evol. 23 12
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